Wannier-Stark flatbands in Bravais lattices

Abstract

We systematically construct flatbands (FB) for tight-binding models on simple Bravais lattices in space dimension $d\ge 2$ in the presence of a static uniform DC field. Commensurate DC field directions yield irreducible Wannier-Stark (WS) bands in perpendicular dimension $d-1$ with $d$-dimensional eigenfunctions. The irreducible bands turn into dispersionless flatbands in the absence of nearest neighbor hoppings between lattice sites in any direction perpendicular to the DC field. The number of commensurate directions which yield flatbands is of measure one. We arrive at a complete halt of transport, with the DC field prohibiting transport along the field direction, and the flatbands prohibiting transport in all perpendicular directions as well. The anisotropic flatband eigenstates are localizing at least factorially (faster than exponential).

arXiv comment11 pages, 3 figures. Similar to the published version. Comments are welcome

References in corpus (37)

• Superfluidity in topologically nontrivial flat bands
• Electronic and optical properties of strained graphene and other strained 2D materials: a review
• Artificial flat band systems: from lattice models to experiments
• Observation of dynamic localization in periodically-curved waveguide arrays
• Geometric origin of superfluidity in the Lieb lattice flat band
• Strongly correlated flat-band systems: The route from Heisenberg spins to Hubbard electrons
• Detangling Flat Bands into Fano Lattices
• Experimental properties of Bose-Einstein condensates in 1D optical lattices: Bloch oscillations, Landau-Zener tunneling and mean-field effects
• Compact localized states and flatband generators in one dimension
• Graphite, graphene and the flat band superconductivity
• Anderson localisation in tight-binding models with flat bands
• Chiral Flat Bands: Existence, Engineering and Stability
• Flat band states: disorder and nonlinearity
• Localization of weakly disordered flat band states
• Preformed pairs in flat Bloch bands
• Landau-Zener Bloch oscillations with perturbed flat bands
• Compactly-supported Wannier functions and algebraic $K$-theory
• Flat-Band Ferromagnetism as a Pauli-Correlated Percolation Problem
• Universal $d=1$ flatband generator from compact localized states
• Flatband generator in two dimensions
• Nonlinear dynamics of Aharonov-Bohm cages
• Nonlinear caging in All-Bands-Flat Lattices
• Topological flat Wannier-Stark bands
• Quantum Caging in Interacting Many-Body All-Bands-Flat Lattices
• Nonlinear localized flatband modes with spin-orbit coupling
• Compactification tuning for nonlinear localized modes in sawtooth lattices
• Low-temperature thermodynamics for a flat-band ferromagnet: Rigorous versus numerical results
• Nonlinear symmetry breaking of Aharonov-Bohm cages
• Disorder perturbed Flat Bands I: Level density and Inverse Participation Ratio
• Compact Discrete Breathers on Flat Band Networks
• Wannier-Stark states in double-periodic lattices I: one-dimensional lattices
• Topological Landau-Zener Bloch Oscillations in Photonic Floquet Lieb Lattices
• Single and double linear and nonlinear flatband chains: spectra and modes
• Cyclotron-Bloch dynamics of a quantum particle in a two-dimensional lattice II
• On Stability of Flat Band Modes in a Rhombic Nonlinear Optical Waveguide Array
• Induced tunneling and localization for a quantum particle in tilted two-dimensional lattices
• Flatband generators

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